That looks like a mustang grapevine, Vitis mustangensis. In time, it is know to smother large trees by growing up into the canopy. You really don't want anything growing near your AC unit because it will restrict air flow.
Luckily, almost all Mulberries are extremely easy to graft. I had someone who had never grafted before do three this year with 100 percent success. They have grown over 10 feet in five months from a 3 inch branch. You can order Mulberry branches "scions" in the winter and graft any variety you want on the seedling. Even the white tasty non-staining variety.